Integrated semigroups and parabolic equations. Part I: linear perburbation of almost sectorial operators

被引：21

作者：

Ducrot, Arnaud ^{[1
,2
]}

Magal, Pierre ^{[1
,2
]}

Prevost, Kevin ^{[3
]}

机构：

[1] Univ Bordeaux, CNRS, UMR 5251, IMB, F-33000 Bordeaux, France

[2] Univ Bordeaux, INRIA Bordeaux Sud Ouest Anubis, F-33000 Bordeaux, France

[3] Univ Le Havre, Dept Math, F-76058 Le Havre, France

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2010年 / 10卷 / 02期

关键词：

Integrated semigroups; Almost sectorial operators; Parabolic equations; Linear perturbation;

D O I：

10.1007/s00028-009-0049-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with linear abstract Cauchy problem with non-densely defined and almost sectorial operators, whenever the part of this operator in the closure of its domain is sectorial. This kind of problem naturally arises for parabolic equations with non-homogeneous boundary conditions. Using the integrated semigroup theory, we prove an existence and uniqueness result for integrated solutions. Moreover, we study the linear perturbation problem.

引用

页码：263 / 291

页数：29

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